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On the relative Morrison-Kawamata cone conjecture (II)

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arxiv 2309.04673 v1 pith:TWA7HIZZ submitted 2023-09-09 math.AG

classification math.AG
keywords conjectureconefinitenessmorrison-kawamataminimalmodelsrelativeweak
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abstract

Assuming the Morrison-Kawamata cone conjecture for the generic fiber of a Calabi-Yau fibration and the abundance conjecture, we show (1) the finiteness of minimal models, (2) the existence of a weak rational polyhedral fundamental domain under the action of birational automorphism groups, and (3) the finiteness of varieties as targets of contractions. As an application, the finiteness of minimal models and the weak Morrison-Kawamata cone conjecture in relative dimensions $\leq 2$ are established.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Boundedness of some fibered K-trivial varieties

    math.AG 2025-07 conditional novelty 8.0 of 10

    Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.

  2. On the Morrison-Kawamata dream space and its applications

    math.AG 2025-12 conditional novelty 7.0 of 10

    An axiomatic framework (MKD spaces) yields deformation-invariance of divisor cones and a conditional boundedness theorem for rationally connected Calabi–Yau varieties.

  3. On the boundedness of elliptic Calabi-Yau 4-folds

    math.AG 2026-07 accept novelty 6.0 of 10

    Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.

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